VOL. XXV-XXVI
THE ARCHIVES OF TRANSPORT
NO 1-2
2013
Interrelation between Wavelengths of Track
Geometry Irregularities and Rail Vehicle
Dynamic Properties
Bogdan Sowinski
Received January 2013
Abstract
The paper deals with the problem of railway track irregularities appearance in form of so-called
short waves (3-25m). These geometrical irregularities were found in measurements, which
were carried out on different railway tracks of Polish Railway Lines. Those tracks can be
classified as tracks with good state of maintenance. The article describes the results of the
analysis of geometrical irregularities of these railway tracks in frequency domain and
demonstrates their statistical characteristics. The studies, in contrast to usually used approach
to the analysis of the geometry of the track, are focused on the left and right rail alignment and
their longitudinal level. Based on studies of different mathematical models of railway vehicles
it was found the relationship between their eigenvalues and wavelengths of track geometrical
irregularities. Analysis of the measurements results of car-body acceleration and bogie frame
acceleration confirms the thesis that the deterioration of railway track is dependent on the
dynamic influences of vehicles on the tracks.
Keywords: short wave irregularities, railway track deterioration, measurements
1. Introduction
The importance of track geometry for studies of railway vehicles dynamic behaviour is
undisputable. Geometric irregularities of a track, such as alignment, cant or gauge,
generate excitations in the system and are a source of vibrations responsible for dynamic
behaviour of the vehicle that moves at high speed on a plain track or an arc of medium or
great value of curve radius. For this reason, modern railway tracks designed for high-speed
traffic should meet a number of requirements regarding travel comfort and safety.
Requirements relating to classification of railway track from the point of view of
geometric irregularities have been the subject of normative acts and a number of scientific

Warsaw University of Technology, Faculty of Transport, Warsaw, Poland e-mail: [email protected]
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Bogdan Sowinski
publications (e.g. [4]). They analyzed methods of defining and describing irregularities for
simulation studies and field tests on the real object. We can mention, among others,
European Standard series EN 13848 “Railway applications – Track – Track geometry
quality” [3], and UIC leaflet 518 [6], [5] or UIC leaflet 714 [7]. They can be treated as
basic normative acts.
The series EN 13848 consists of six parts. It covers the wide-ranging problems of
classifications irregularities, their recording, measurements and used measuring devices.
Part 1 entitled “Characterisation of track geometry” specifies characteristics of track
geometry such as e.g. track gauge, longitudinal level, alignment, cross level and twist.
Parts 2 – 4 entitled “Measuring systems – Track recording vehicles”, “Measuring
systems – Track construction and maintenance machines” and “Measuring systems –
Manual and lightweight devices” give hints concerning track recording vehicles, track
maintenance machines and manual devices.
Part 5 entitled “Geometric quality levels” defines the quality levels of the track
geometry. They are called: Alert Limit (AL), Intervention Limit (IL) and Immediate
Action Limit (IAL).
UIC standard 518 sets also three quality levels with similar meaning of AL, IL and IAL
but with different names: QN1, QN2 and QN3 respectively.
QN1 quality level (AL – Alert Limit), which refers to the value which necessitates
monitoring or taking maintenance actions as part of regularly-planned maintenance
operations;
QN2 quality level (IL – Intervention Limit), which refers to the value that requires short
term maintenance action;
QN3 quality level (IAL – Immediate Action Limit), which refers to the value above
which is no longer desirable to maintain the scheduled traffic speed.
These quality levels boundaries base on thresholds connected to standard deviation of
longitudinal level defects.
A set of new track quality indices has been developed in USA [2]. In this work and [9],
authors sum up characteristics of track irregularities into a track quality index, which is
function of the standard deviations of irregularity, and train allowable speed. The
considerations shown in that work can be treated as the complement of the tracks
classification based on the Federal Track Safety Standards [8]. According to them, there
are distinguished nine classes of tracks. For each class is defined the maximum allowable
speed for freight and passenger trains. Classification takes into account deviation of track
dimension from nominal values and shape of rails rolling surfaces.
It is also worth to notice that there are normative acts, which define the shape and
dimension of railway track geometric irregularity, which should be applied in simulation
studies [1].
The so-called short wavelength (3 m – 25 m) [3] longitudinal levelling defects are still
the crucial parameters for the railway track maintenance and it is pointed in the abovementioned references. As it is shown in this paper, the problem of such irregularities also
exists in the Polish railway infrastructure. There were done several measurements in
different sections of railways lines of Polish Railways Lines. These measurements covered
Interrelation between wavelengths of track geometry irregularities and rail vehicle ...
99
the track distance of a length of 500 m each. Basing on them, there were reached the
conclusions, which are associated with dominant wavelengths of geometrical irregularities
of the track. It was shown that the wavelengths of these irregularities correspond to the
allowable velocity of trains in those track sections and they correspond to eigenvalues of
wagons, which operate on those lines also. Analysis of the results of acceleration
measurements of a carbody and a bogie frame also confirms the thesis that the
deterioration of railway track is related to the influences of vehicles on the track within a
specific frequency range and therefore the constructional characteristics of the vehicles,
which have been operated on the track.
2. Measurement Methods of Railway Track
Geometric Irregularities
Analyzed in this paper irregularities were measured with the track geometry measuring
trolley and the measuring vehicle.
Track geometry-recording car EM-120 allows to record such track geometric
irregularities as longitudinal level and alignment on both sides of the track, twist, gauge
and cant. These parameters are registered at 0.25 m.
The track geometry measuring trolley is a portable device designed for collecting and
recording information on railway track geometric features in form of a set of readings
recorded in digital form.
In both cases the input data are recorded automatically during the passage of the device
along the track.
In our case, all measurements are sampled at constant distance based intervals equal to
0.5 m and resolution of measurement is 0.1 m. Measuring range of track gauge is from
1420 up 1485 mm with resolution equal to 0.1 mm. The same resolution is assumed for
cant, level and alignment. The range of measurement is equal ± 50 mm. The range of
measured irregularity wavelength, i.e. 5 to 25 m (in case of measurements done with
measuring trolley), may be approximately estimated as the range of short railway track
irregularity (class D1 [3]).
3. Irregularities Statistical Analysis
Track irregularities, which are discussed in detail in this paper, were recorded in
sections of line between Warsaw and Poznan (called here measurement 1, measurement 2,
measurement 3), in a section of Warsaw-Cracow line (called measurement 4) and in a
section of the line between Warsaw and Gdansk (measurement 5). Measurement 1 and
measurement 2 were made on the same track in a time interval of around four months.
The first step of the adopted preprocessing was an elimination of abnormal data and
then there was done the normalization of recorded data relative to the average, so it is
equal to zero.
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Bogdan Sowinski
According to [3] there were done calculations of nominal track gauge peak to peak
value, mean to peak value of longitudinal level and alignment, standard deviation of
longitudinal level and alignment of measured tracks. We can say, basing on those
calculations, although they are not complete, that investigated tracks have more or less
track quality AL or QN1 for train speed less than 200 km/h and wavelengths class D1.
Studies on irregularities presented in this paper are focused on left and right rail
alignment and their longitudinal level.
The processing of the transformed measurement results concentrated on calculation of
the range of the variation of vertical and lateral irregularities of rails, their standard
deviations and power spectral densities expressed as functions of irregularity wavelength.
In tables 1 and 2 are presented basic statistical parameters of rails irregularities.
Table 1
Standard deviations of left and right rails in measured track sections
Measurement no
1
2
3
4
5
Irregularities Standard Deviations [m]
Vertical Irregularity
Lateral Irregularity
left rail
right rail
left rail
right rail
0.00113
0.00120
0.00137
0.00127
0.00135
0.00137
0.00199
0.00153
0.00109
0.00101
0.00135
0.00153
0.00115
0.00120
0.00103
0.00108
0.00155
0.00132
0.00168
0.00167
Table 2
Irregularities variation range of left and right rails in measured track sections
Irregularities Range [m]
Measurement no
1
2
3
4
5
Vertical Irregularity
left rail
right rail
0.0108
0.0111
0.0134
0.0127
0.0089
0.0089
0.0073
0.0073
0.0108
0.0099
Lateral Irregularity
left rail
right rail
0.0091
0.0077
0.0123
0.0089
0.0091
0.0112
0.0055
0.0056
0.0113
0.0091
The worst statistical values were obtained for measurement 5, although they are also
moderate.
Now we will show examples of results for the power spectral density of irregularities on
the tested tracks sections. Examples present results obtained for three different lines. In
figures 1 – 3 are presented PSD results for vertical irregularities of rails.
Interrelation between wavelengths of track geometry irregularities and rail vehicle ...
Comparison of PSD of vertical irregularities
2
[m] /[1/m]
Left rail PSD
2·10
-5
2·10
10
Right rail PSD
-5
-5
-6
8·10
-6
4·10
0
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
[1/m]
Fig. 1. Power spectral density of vertical irregularities for measurement 1
Comparison of PSD of vertical irregularities
Left rail PSD
Right rail PSD
2
[m] /[1/m]
-5
10
-6
8·10
-6
6·10
-6
4·10
-6
2·10
0
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
[1/m]
Fig. 2. Power spectral density of vertical irregularities for measurement 4
Comparison of PSD of vertical irregularities
Left rail PSD
Right rail PSD
2
[m] /[1/m]
-5
8·10
-5
6·10
-5
4·10
-5
2·10
0
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
[1/m]
Fig. 3. Power spectral density of vertical irregularities for measurement 5
The analysis of obtained results we will begin with vertical irregularities.
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Bogdan Sowinski
Recorded results for measurement 1 (fig. 1) show that wavelengths of irregularities are
included in the range between ~8 and ~50 m. Irregularities for left and right rail are
comparable with the high correlation coefficient. Peaks of PSD are located in almost the
same position for left and right rail, although they are clearly marked for right rail.
Dominant wavelengths are equal to ~33, ~14 and ~12 m.
Wavelengths of irregularities for measurement 2 are analogous, however the third peak
splits into three peaks situated closely to each other.
For measurement 3, the irregularities wavelengths are included between ~7 and ~50 m.
Peaks are not so clearly marked as in previous case, but we can also select dominant
wavelengths approximately equal to 30, 16.5 and 14.5 m for both rails.
The level of PSD for measurement 4 (fig. 2) is smaller than in previously considered
examples. Considering this fact, we can say that wavelengths irregularities are included in
the range between ~7 and ~25 m. In PSD diagram we can distinguish wavelengths equal to
18, 16 and 9.5 m. Some peaks of PSD for left and right rail have different locations.
In the last measurement (fig. 3), the distinct peak is situated for wavelengths
approximately equal to 12.5 m. There are also easy to detect peaks for 25 and 8 m.
In figures 4 – 6 are presented some results for lateral irregularities of rails.
Comparison of PSD of lateral irregularities
Left rail PSD
Right rail PSD
2
[m] /[1/m]
-5
1,5·10
-5
1,2·10
-6
9·10
-6
6·10
-6
3·10
0
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
[1/m]
Fig. 4 Power spectral density of lateral irregularities for measurement 1
Interrelation between wavelengths of track geometry irregularities and rail vehicle ...
103
Comparison of PSD of lateral irregularities
Left rail PSD
Right rail PSD
2
[m] /[1/m]
-5
3,5·10
-5
2,8·10
-5
2,1·10
-5
1,4·10
-6
7·10
0
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
[1/m]
Fig. 5. Power spectral density of lateral irregularities for measurement 4
Comparison of PSD of lateral irregularities
Left rail PSD
Right rail PSD
2
[m] /[1/m]
-5
4·10
-5
3,2·10
-5
2,4·10
-5
1,6·10
-6
8·10
0
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
[1/m]
Fig. 6. Power spectral density of lateral irregularities for measurement 5
Having analyzed results presented above (examples on figures 4 – 6) we can conclude
that they are easier for the interpretation.
Dominant wave of measurement 1 is ~17 m long (fig.4) and for measurement 2 is 32 m.
Waves, with a length of ~11 and ~18 m, dominate in the third measurement. Single,
very well distinguished wave of length equal to ~10 m dominate in the fourth measurement
(fig. 5.). We can conclude that the PSD’s of the right and left rails are characterized by a
high degree of similarity in the measurement. Such fact is not observed for results found
for the fifth measurement. The dominant waves for left rail have lengths in the range from
~25 m to ~55 m. Dominant wave for right rail is ~13 m long.
The range of irregularities wavelengths covers the interval ~7,5 m to ~50 m in all
studied cases.
We will deal with the waves with length, which does not exceed 30 m, because of the
adopted measurement method.
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Bogdan Sowinski
The fundamental problem in irregularities study is to answer the question if such
irregularities can cause derailment of the car or decrease the ride comfort.
Both facts are related to the frequency of excitation. Alignment wavelength, which
causes vibrations close to the resonance of lateral motion of a bogie frame or carbody, may
be the derailment reason and specific wavelength of the longitudinal level may decrease
the ride comfort.
Therefore, the fundamental problem is to determine whether the measured irregularities
cause excitations in the railway vehicle – track system that are close to the resonant states
of cars.
Passenger trains operate with velocity from 140 km/h to 160 km/h on studied railway
lines and freight trains with velocity from 60 km/h to 80 km/h.
These speeds result in excitation frequencies range from ~ 1.3 to 6.4 Hz.
Finally, it is necessary to mention about results, that were obtained for measurements
made over the same track section. They show the growth of statistical parameters, very
similar power spectral density function and moreover very high Pearson coefficient (equal
to 0.94).
4. Description of Rolling Stock Characteristics
In this paragraph are described typical models of wagons, which operate on the Polish
railways. There was done analysis of these models eigenvalues. In addition, the frequency
analysis of recorded vertical and lateral acceleration of the carbody and the bogie frame
was performed.
As mentioned above, passenger and freight wagons operate on measured routes. It is not
possible to build their mathematical models because of the diversity of their construction.
Therefore, there were used their abstractions which were built for a passenger car, a freight
car and a locomotive.
Abstractions of vehicles have been modelled using Virail package.
General assumptions for modelling were that suspension characteristics are linear and
the contact between wheel and rail is linear. It is based on equivalent geometric parameters
of rail (UIC60) and wheel (S1002) such as wheel equivalent conicity and gravitational
stiffness.
Passenger car model is composed of rigid bodies such as car body, two bogie frames
and four wheelsets. Elements of primary and secondary suspensions are assumed massless.
Model parameters (geometry, inertia, stiffness and damping) are similar to those used in
typical models of passenger railcars of European carriers.
Parameters of locomotive model respond to EP-09 locomotive. It is a discrete model
consists of 15 rigid bodies: the body, two bogie frames, four wheelsets and eight axleboxes. Rigid solids are connected with massless elastic–damping suspensions. The
exceptions are connections of wheelsets with axle-boxes. Those elements allow only for
the rotations of the wheelsets.
Interrelation between wavelengths of track geometry irregularities and rail vehicle ...
105
The parameters and the structure of the freight car model have been adopted on the
basis of technical data four-axle type Eanos wagon. Bogie parameters specification is
based on freight bogie 6RS/N parameters.
Interaction between railway car and track irregularities depends mainly from
eigenvalues of the vehicle and the frequencies of excitations i.e. train operation speed and
wavelengths of irregularities.
Eigenfrequencies of models are presented in table 3.
Table 3
Eigenfrequencies of railway vehicles mathematical models connected with their carbodies
and bogies
Vehicle element
carbody
bogie
Motion
lateral displacement
bounce
roll
pitch
yaw
lateral displacement
bounce
roll
pitch
yaw
Passenger car
f [Hz]
0.50
1.09
1.37
1.44
0.70
4.88
5.25
5.23
6.48
7.52
Locomotive
f [Hz]
0.43
1.05
1.56
0.97
0.66
6.61
4.13
4.83
5.23
6.25
Loaded freight car
f [Hz]
0.44
0.84
1.26
0.92
0.77
4.63
4.81
5.11
5.45
7.47
The eigenfrequencies of the horizontal movements of the vehicle on the track are in the
range from ~0.43 Hz to 0.77 Hz for the carbodies and from ~4.63 to 7.52 Hz for the
bogies. The eigenfrequencies of the vertical movements of the vehicle on the track are in
the range from ~0.84 Hz to ~1.56 Hz for the carbodies and from ~4.13 to 6.48 Hz for the
bogies.
Now we will present the results of measurements of the passenger car equipped with
MD bogie type. Measurements were performed with the vehicle velocity equal to 160 km/h
on well-maintained track. Results obtained for vertical motions are shown in figures 7 and
8 and for lateral motions in figures 9 and 10.
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Bogdan Sowinski
Comparison of PSD of carbodies vertical accelerations
Second measurement
22
[m/s ] /[Hz]
First measurement
0,03
0,02
0,01
0
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
2,2
2,4
2,6
2,8
3
3,2
3,4
3,6
3,8
4
[Hz]
Fig. 7. Power spectral density of vertical carbody acceleration
Comparison of PSD of bogies frames vertical accelerations
22
[m/s ] /[Hz]
First measurement
Second masurement
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
0
2
4
6
8
10
12
14
16
18
20
[Hz]
Fig. 8. Power spectral density of vertical bogie frame acceleration
Interrelation between wavelengths of track geometry irregularities and rail vehicle ...
107
Comparison of PSD of carbodies lateral accelerations
Second measurement
22
[m/s ] /[Hz]
First measurement
0,012
0,009
0,006
0,003
0
0,6
0,8
1
1,2
1,4
1,6
1,8
2
2,2
2,4
2,6
2,8
3
3,2
3,4
3,6
3,8
4
[Hz]
Fig. 9. Power spectral density of lateral carbody acceleration
Comparison of PSD of bogies frames lateral accelerations
Second measurement
22
[m/s ] /[Hz]
First measurement
0,06
0,04
0,02
0
0
2
4
6
8
10
12
14
16
18
20
[Hz]
Fig. 10. Power spectral density of lateral bogie frame acceleration
Results obtained from experiments show that maximal vertical carbody accelerations
are situated between ~0.9 – 1.7 Hz. It responds, if vehicle speed equals to 160 km/h, the
wavelength range from ~27 to 50 m. Frequencies of maximal bogie frame vertical
acceleration are included in the interval ~5 – 16 Hz i.e. ~3 – 11 m of wavelength.
These ranges for the lateral vibrations are respectively ~18 – 50 m and ~8 – 15 m.
5. Conclusions
Explanation of appearance of a railway track geometric irregularities and their increase
decisively influence the track maintenance optimisation.
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Bogdan Sowinski
The newly built or just after the renovation railway line is theoretically an ideal
geometrical straight line or a curve. In practice, track geometry is always imprecise. Every
rails joint introduces disturbances of shock type in vehicle vibrations and besides those;
there are special track sections like crossings or turnouts where track geometry causes
transient vehicle vibration. Resulting forces, acting on the track, vary with the frequencies
corresponding to the vehicle eigenfrequencies and affect the different level of track
degradation. Finally, the track geometry damages progressively. The appearing
irregularities are thus characterized by a short wavelength (class D1 [3]) i.e. between 3 and
25 m whereas the geometry of new tracks is characterized by long wavelengths (class D3
[3]).
This range of irregularities wavelengths depend mainly on the dynamical action of a
bogie on the track and speed of vehicles exploited on the railway.
The appearing irregularities may be different for different railway lines depending on
the rolling stock being in operation on them. However, it appears that the track
irregularities wavelengths depend on the rolling stock initially operated on a railway line.
Measurements made on the same track indicate this fact, that the wavelengths of
irregularities did not change, but their amplitudes are changed.
References
1. DOT/FRA/ORD-01/05: Safety of railroad passenger vehicle dynamics. Final Summary Report.” Office of
Research and Development Washington, DC 20590 U.S. Department of Transportation. 2002.
2. El-Sibaie, M., Zhang, Y-J.: Objective track quality indices. Transportation Research Record, vol. 1863,
pp. 81-87 ISBN 0-3090-9456-9, 2004.
3. EN: European Standard EN 13848-1-6: Railway applications – Track – Track geometry quality. European
Committee for Standardization (CEN). ISBN: 97-8058-069-07-30, 2008.
4. Esveld, C.: Modern Railway Track. MRT-Productions. 2nd Edition ISBN 90-8004-324-3-3, 2001.
5. UIC: Best practice guide for optimum track geometry durability. ISBN 2-7461-1456-9, 2008.
6. UIC 518 Leaflet: Testing and approval of railway vehicles from the point of view of their dynamic
behavior – Safety - Track fatigue - Ride quality. 3rd edition, 2005, ISBN 2-7461-0353-2, 2005.
7. UIC 714 Leaflet: Classification of lines for the purpose of track maintenance. 4th edition, ISBN 978-27461-1162-4, 2009.
8. Track and Rail and Infrastructure Integrity Compliance Manual, 2012.
9. Zhao, J., Chan, A.H.C., Roberts, C. and Stirling, A.B.: Optimizing Policies of Railway Ballast Tamping
and Renewal. Transportation Research Record: Journal of the Transport Research Board, No. 1943,
Transportation Research Board of the National Academies, Washington, D.C., pp. 50-56, 2006.
Acknowledgements
The authors express their gratitude for the financial support by the Polish Ministry of Science and
Higher Education for the support of research within the framework of the project No N N509
538440.